When several bodies move together — two blocks in contact being pushed, a train of carriages, a pulley with two connected masses — we are often not interested, in the first instance, in knowing the forces they exchange internally, but only in the common acceleration of the whole. In these cases it is convenient to treat the entire group of bodies as a single system and apply Newton’s second law to it.
Principle — Second law for a system
where is the common acceleration (if the bodies move together). The internal forces cancel out.
The key to the method lies precisely in the last sentence: the internal forces — those that the bodies of the system exchange with one another — cancel out in pairs. This is a direct consequence of Newton’s third law: every internal force is accompanied by its twin, equal and opposite, also internal to the system. Summing all the forces acting on the bodies of the system, every internal action–reaction pair contributes zero, and only the external forces survive, that is, those exerted by bodies that are not part of the system. On the right-hand side of the equality appears the total mass, simply the sum of the masses of the individual bodies.
Tip
Writing the second law for the system gives the acceleration directly, without having to deal with the internal forces. Once is known, one returns to the single body, applies the second law to it again, and derives the internal forces sought.
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Topics: Dinamica Concepts: Seconda legge di Newton Skills: Diagramma di interazione
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